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Ray traces in a distributed-index planar microlens.

K Iga¹, M Oikawa, J Banno

¹Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan.

|April 17, 2010

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This study presents a ray-optical method for analyzing planar microlenses with complex refractive index profiles. The developed technique enables accurate estimation of optical properties like focal length and spherical aberration.

Area of Science:

Optics and Photonics
Micro-optics
Ray Optics

Background:

Planar microlenses are crucial optical components.
Accurate modeling of refractive index distributions is essential for predicting microlens performance.
Existing methods may not fully capture the complexities of 3-D distributed refractive indices.

Purpose of the Study:

To develop a ray-optical treatment for planar microlenses with 3-D distributed refractive indices.
To derive an analytic form of the ray trace for specific index profiles.
To estimate key optical properties of planar microlenses.

Main Methods:

Derivation of an integral form of the ray equation.
Expressing the refractive index distribution as a sum of functions of radial (r) and axial (z) distances.

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Solving the integral equation independently for r and z.

Applying the derived ray trace to planar microlenses with approximated index profiles.

Main Results:

An analytic form of the ray trace was obtained for specific refractive index distributions.
The method allows for the estimation of optical properties.
Key optical parameters such as focal length, numerical aperture, and spherical aberration were estimated.

Conclusions:

The presented ray-optical treatment provides an effective method for analyzing planar microlenses with 3-D refractive index distributions.
The analytic solutions simplify the prediction of microlens performance.
This approach is applicable to fabricated devices with index profiles that can be approximated by the assumed model.